A note on the second-order non-autonomous neutral stochastic evolution equations with infinite delay under Carathéodory conditions. (English) Zbl 1410.60059
Summary: In this note, we aim to study a class of second-order non-autonomous neutral stochastic evolution equations with infinite delay driven by a standard cylindrical Wiener process and an independent cylindrical fractional Brownian motion with Hurst parameter \(H\in(1/2,1\)), in which the initial value belongs to the abstract space \(B\). We establish the existence and uniqueness of mild solutions for this kind of equations under some Carathéodory conditions by means of the successive approximation. The obtained result extends some well-known results. An example is proposed to illustrate the theory.
MSC:
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 34F05 | Ordinary differential equations and systems with randomness |
Keywords:
second-order neutral stochastic evolution equation; non-autonomous; infinite delay; Carathéodory conditionReferences:
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